The Pedagogical University is located at the city centre close to most historic monuments and attractions, so you can do some sightseeing during lunch time:
1.    Golden Gate + St.Sophia (Volodymyrska Street)
2.    Andriivsky Uzviz
3.    Khanenko Art Museum (15-17 Tereshchenkivska Street)
4.    Volodymyrska Hill + Mykhailivsky Cathedral
5.    Volodymyrsky Cathedral (Shevchenko Boulevard)
6.    Central Park + government district (Hrushevsky Street)
7.    Kyivo-Pecherska Lavra (only monastery and caves) - take bus No. 24 from Khreshchatyk (on the opposite side from the Central Department Store). The entrance to the museum is located at the Gate Church. The way to the monastery is farther - you'll see a lane down with guards' booth. Go down the lane to the monastery. Please no shorts/open clothes. Women will not be allowed to enter caves without a shawl. The entrance is free - but you'll have to buy a candle (electricity was removed from the caves when they were returned to a monastery).
8.    Khreshchatyk Street from Bessarabska Square to Evropeyska Square and back + Bessarabsky Market  (you can sample some nice cottage cheese, pickles and 'salo' (pork fat))
9.    Ukrainian Art Museum (Evropeyska Square)

Longer excursions (4-8 hours)
1.    Kyivo-Pecherska Lavra (museums + monastery), then the Second World War monument (you can go up the figure of the monument) and museum
2.    Babyi Yar + St.Cyril Church (XI century building, paintings by M.Vrubel (XIX century) - metro Dorogozhychi (see monument in Babyi Yar near the metro station), then take a trolleybus No.27 or any minibus from the metro station to St.Cyril Church (ask for Kyrylivska Tserkva). If you have more time after visiting the church, the same trolleybus will take you to Petrivka book market (then you can go back by metro from Petrivka).
3.    Volodymyrska Street - Andriivsky Uzviz (Descent) - Kontraktova Square - Sahaidachny Street - River Port  (back by metro from Poshtova Ploshcha)
4.    Central Botanical Garden + Illynska Church + Vydubitsky Monastery- to metro Pecherska, then go to the end by trolleybus/minibus No.14 from the stop on the opposite side of Lesya Ukrainka monument. Ask for Botanichny Sad.
5.    Kytayevo Monastery and caves - minibus 412 from Tolstoy Square, stop near ProCreditBank. It is not a tourist spot but a monastery and cathedral serving as a praying and pilgrimage place for believers. Go to Kytaivska Street (20-30 minutes drive), then ask for the monastery.
Estimated time needed to visit all major sights is two weeks.

Museums
Ukrainian museums are very traditional with no high-tech shows. Information in English is usually not available, but it in most museums it is possible to book a guided tour in English. Museums do not have cafes (except Open Air Museum), so it may be a good idea to eat before the visit. Museums normally stop selling tickets one hour (sometimes 30 minutes) before closing time.

St. Sophia (XI century church with mosaics - this is an absolute must to be seen in Kyiv + several other museums and exhibitions)
24 Volodymyrska Street, every day 10.00-18.00, Friday and Saturday until 19.00.   
The 13-domed cathedral was built by Prince Yaroslav the Wise in 1037 and named after St. Sophia's Cathedral in Constantinople, to glorify the wisdom of Christianity. It has fantastic mosaics and frescoes from that time. The cathedral was a main place of worship and a major cultural and political centre in Kyiv Rus. The belfry was built in 1744-1752.

Kyivo-Pecherska Lavra - another must-see place http://en.kplavra.kiev.ua/
21 Sichnevoho Povstannya Street, 09.00-17.00 (tickets are sold until 17.00).  
The monastery was established in 1051. You can visit the caves with underground churches where monks lived and were buried (this is at the territory of the monastery and is not a museum) and many other churches and museums: Gold Treasury (Scythian gold collection), Ukrainian Folk Art Museum, Books and Printing Museum,  Theatre Museum, the Miniatures Museum. If you feel a need for an exercise and/or wish to see a beautiful view of the city, climb the bell tower (105 m). The 12th century Uspensky (Dormition) Cathedral was blown up in 1941 in an unsuccessful attempt of a KGB agent to kill a German officer (the officer survived, the cathedral and many locals inside did not). It was replicated in 2000.

National Art Museum of Ukraine http://namu.kiev.ua/en.html
6 Hrushevsky Street, Wednesday, Thursday, Sunday 10:00-18:00; Friday 12:00-19:00; Saturday 11:00-19:00

Khanenko Art Museum (Western European art) http://khanenkomuseum.kiev.ua/
15-17 Tereshchenkivska Street, 10.30-17.30, closed Monday, Tuesday
Russian Art Museum http://www.kmrm.com.ua/eng
9 Tereshchenkivska Street, Wed, Sat, Sun 10.00-18.00, Tue,  Fri – 11.00-19.00 (tickets are sold until one hour before closing time); closed Monday, Tuesday

Open Air Museum (restored traditional Ukrainian villages) http://pyrohiv.com.ua/en/
Pyrogovo village (metro “Vystavkovyi Centre”, then trolleibus No.11 to the end), 10.00-17.00
(it is better to go there for at least 4 hours, travelling there by public transport is approximately 1 hour one way).

Other interesting museums: Golden Gate; History Museum (near Andriyivska Church); Taras Shevchenko Museum (corner of Tereshchenkivska Street on the left from the Institute), Literature Museum (corner of Tereshchenkivska Street on the right from the Institute); Museum of One Street (Andriyivsky Uzviz); Mikhail Bulgakov Museum (Andriyivsky Uzviz); lots of modern art galleries.

Theatres/Concerts

Classical music
National Philharmonic - 2 Volodymyrsky Uzviz (Evropeyska Square) http://www.filarmonia.com.ua/en.afisha
Tickets are sold in the box office of the National Philharmonic
and can be bought before the concert

Classical music concerts - Kyiv House of Organ and Chamber Music http://www.organhall.kiev.ua/component/option,com_shedule/Itemid,59/lang,en/
77 Chervonoarmiyska Street, metro "Tsentralny Stadion"
Concerts start at 19.30
Tickets can be bought at the theatre ticket booth at Bohdan Khmelnytsky Street near the Institute of Mathematics. At the same place you can see all theatre and concert repertoires and buy tickets (except for National Philharmonic).

Churches
Before the October revolution in 1917 Kyiv was a city of churches with many places of pilgrimage. 1930s was the time when many churches and monasteries were destroyed or transformed into something else (atheism or art museums, concert halls, cinema theatres, warehouses, facilities for physical experiments). It happened not only with churches but also with anything religious. The Brodsky synagogue was a puppet theatre until it was recently restored to its original function.
After 1990 many former churches were given to respective religious communities, restored and reconstructed. E.g. existing Mykhailovsky Cathedral (originally from XI century) is a replica built in 1999. The only preserved buildings from huge monastery complex are small refectory church and former hotel/residential premises. The cathedral was destroyed in 1930s with the aim to build a biggest square for Soviet administrative buildings. The only implemented building from this plan is a grey structure with columns on the left from the cathedral that how houses the Ministry of Foreign Affairs of Ukraine. The big plan also envisaged destroying of St.Sophia that was saved by French government that gave the Soviet Union some prize for its preservation as a French cultural heritage monument (Anna, Prince Yaroslav's daughter, whose picture can still be seen at one of St.Sophia frescoes, became a queen of France, obviously by marriage. Thus she saved St.Sophia some 9 centuries later, and it remained as a real thing (though rebuilt on the outside in 16th century).
Building of the new old churches (replicas) is a rather controversial issue in Ukraine, even if not to question appropriateness of spending large amounts of money in a country with no money for adequate healthcare. These churches are not built under old schemes (that would require thirty years and lots of eggs for making mortar) and look as what they are - replicas. However, the Mykhailovsky Cathedral looks nice and really completes the square. At present new churches are also built - especially in new residential districts in the outskirts, and in large hospitals.
Most churches are not museums but actually churches, and they do not charge admission fees but require complying to certain etiquette with no exception made for tourists. Women planning to visit churches, monasteries and monastery caves anywhere in Ukraine (especially those of Russian Orthodox Church of Moscow Patriarkhate, e.g. caves in Kyivo-Pecherska Lavra and Kytayevo) are strongly advised to take shawls with them as they may be literally not allowed to enter. Shorts, short skirts and open tops will not be allowed; trousers for women are not advised. Ukrainian Orthodox Church is more tolerant, so a woman may go (but better not to) to Volodymyrsky or Mykhailovsky Cathedral without a shawl and in a short skirt. Men are supposed to remove their hats in churches, and avoid shorts. Talking (and excursions) is not allowed in churches. St.Sophia is a museum (a religious community cannot ensure its preservation, and services are held there extremely rarely for special occasions), so excursions are possible. All churches welcome donations for their restoration. Functioning orthodox churches are not used for concerts. Services in main churches are held at 9 a.m. and 6 p.m.
There are also numerous places of worship of other confessions.

Monuments
Monuments of different epochs are quite numerous. Lenin at the beginning of Shevchenko Boulevard was preserved as "piece of art", so it remains the place for putting flowers on appropriate days for existing communists and socialists. Another Lenin monument that used to occupy the place of the present large glass gallery with Ukraine hotel at the background was in Maidan Nezalezhnosti, then October Revolution Square, and was removed in 1991. A Soviet time monument that did not lose its moment in the least is the monument to great Ukrainian philosopher Hryhoriy Skovoroda in Kontraktova Square. His two most famous sayings are "The world tried to catch me but had not caught" and "Anything necessary is simple, anything that is not simple is unnecessary" (very relevant in mathematical physics).
There are several major monuments to those died in the Second World War - Eternal Fire in the Park of Glory (Slavy Square), Motherland in the Second World War Museum and monument to those who died in Babyi Yar.
The place near Taras Shevchenko monument (opposite the Red Building of the Kyiv Shaevchenko National University) is famous as a location of opposition meetings both in the Soviet times and at present. Recital of Shevchenko poems there in 1960s actually got people to prison. The situation was quite absurd - the same poems were studied at schools.
An example of 19th century monuments are St.Volodymyr ar Volodymyrska hill (above Evropeyska Square) and Bohdan Khmelnytsky in Sophia Square.
New times brought the monument to Mykhailo Hrushevsky, the first president of Ukraine (in 1918, during brief independence period), in the corner of Shchevchenko Boulevard and Volodymyrska Street, to Ukrainian hetman (military leader) Sagaidachny in Kontraktova Square and many small "chamber" monuments to real and imaginary people. One such monument to a literature hero is located at Prorizna Street. Panikovsky is a hero of humour book by Russian writers Ilf and Petrov "Golden Calf", and was known in the book as a blind beggar, famous before the October Revolution, who worked at just this place, asking people to take him across the street and picking their pockets in the process. The idea of putting a monument to a beggar and petty thief may seem strange, but in fact it is a monument to a great book and to a great actor Zinoviy Gerdt who played Panikovsky in the "Golden Calf" screen version.

Hidden treasures
Ukraine (and Kyiv) is a hidden tourist treasure in itself, but still there are numerous extremely interesting places not mentioned in guidebooks at all. We can name Kytayevo Monastery, St. Pantheleimon Monastery with holy spring (Feofaniya near the Institute of Theoretical Physics and the Open Air Museum), Zvirinetsky caves, Hnyletsky caves (not open for the general public yet, and organisation of special tours is not practical at a large conference), Frolovsky Monastery (Podil near Kontraktova Square), Pokrovsky Monastery (Bekhterevsky Lane), hills around Andriyivsky Uzviz with old cemeteries, small streets in Podil between Sahaidachny Street and the Dnieper embankment, old wooden churches in new residential districts that remained from the times when these districts were villages. There are more to see in historic places around Kyiv - e.g. Nizhyn - two hours by suburban train or Chernihiv (two or three hours by bus), Pereyaslav-Khmelnytsky (2 hours by bus), parks in Bila Tserkva and Sofiyivka.
Links
Kyiv at UNESCO site http://whc.unesco.org/sites/527.htm
Art museums http://www.ukrtravel.com/kiev_museums.htm
http://www.kiev.info/culture/museums.htm

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